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Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 51 Issue: 3

Bi-periodic $r$-Fibonacci sequence and bi-periodic $r$-Lucas sequence of type $s$

Nacima Rosa Aıt-amrane(USTHB)0000-0002-0241-996X
Hacène Belbachir(USTHB)0000-0001-8540-3033
Pages
—
Publication Date
2022-06-01
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⚡ TL;DR(Too Long; Didn't Read)

Furthermore, we give their properties as linear recurrence relations, generating functions, explicit formulas and Binet forms.

📌 3 Key Takeaways

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Objective & Hypothesis:In the present paper, for a positive integer $r$, we study bi-periodic $r$-Fibonacci sequence and its family of companion sequences, bi-periodic $r$-Lucas sequence of type $s$ with $1 \leq s \leq r$, which extend the classical Fibonacci and Lucas sequences.
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Key Findings & Data:Afterwards, we establish the link between the bi-periodic $r$-Fibonacci sequence and its companion sequences.
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Conclusion & Impact:Furthermore, we give their properties as linear recurrence relations, generating functions, explicit formulas and Binet forms.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:bi-periodic r-Fibonacci sequence · bi-periodic r-Lucas sequence · companion sequence

Abstract

In the present paper, for a positive integer $r$, we study bi-periodic $r$-Fibonacci sequence and its family of companion sequences, bi-periodic $r$-Lucas sequence of type $s$ with $1 \leq s \leq r$, which extend the classical Fibonacci and Lucas sequences. Afterwards, we establish the link between the bi-periodic $r$-Fibonacci sequence and its companion sequences. Furthermore, we give their properties as linear recurrence relations, generating functions, explicit formulas and Binet forms.

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Cite This Article

Aıt-amrane, N. R., Belbachir, H. (2022). Bi-periodic $r$-Fibonacci sequence and bi-periodic $r$-Lucas sequence of type $s$. Hacettepe Journal of Mathematics and Statistics, Volume: 51 Issue: 3. https://doi.org/10.15672/hujms.825908

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